Canada international Edgar arrived for a second loan spell at Swansea on transfer deadline day, but while the Football League and Football Association of Wales ratified the move, FIFA blocked it due to a simple administrative error.
Jenkins said: "We were told there was one decimal point out of place on Burnley's paperwork, a meaningless decimal point, and it has been extremely frustrating ever since trying to get FIFA to approve the loan deal.
"As a football club we feel it's an injustice that when we sign a player from a British club that plays in the same domestic league as us, then only ourselves and Cardiff City have to go through the process of getting international clearance.
"It used to be a fairly simple process between the two associations until FIFA came up with this new online system. It seems to have caused a lot of problems for a number of clubs.
"Despite the fact that both the Football League and FAW are happy to sanction the move, dealing with FIFA has been a nightmare. It's been very hard to get any answers from them and they're certainly not in any rush to get the matter resolved."